Modern communication systems, especially wireless communication systems, in order to provide enhanced performance in terms of packet error rate (PER) over selective fading communications channels, make use of advanced iterative equalization and decoding techniques. These schemes may include Turbo Equalization (TEQ) when a single stream (SISO) is transmitted and received, and Parallel or Successive Interference Cancellation (PIC or SIC, respectively), when multiple streams are transmitted and detected over MIMO (Multiple In Multiple Out) channels. In all the above iterative equalization and decoding schemes, when deployed in the receiver, all except the 1st iteration make use of the improved LLRs (Log Likelihood Ratios) obtained from the FEC (Forward Error Correcting) decoder output at the end of the previous iteration(s). This feedback information, improved LLR stream, is used to eventually compute estimated QAM symbols corresponding to the stream. These estimated QAM symbols, in combination with an estimated channel matrix, provide a basis for estimating and removing the interference caused by the stream from the received signal on the next iteration of equalization and decoding.
The aforementioned estimation of QAM symbols, or soft-modulation, includes computing probabilities from LLRs for each transmitted bit, then computing ‘soft’ QAM symbols from each K bit probabilities, with M=2K being the constellation order (K=2 for QPSK, K=4 for 16QAM, K=6 for 64 QAM, K=8 for 256QAM). A straight-forward approach to the soft modulation would involve a computational complexity growing exponentially with K (linearly in M). Since soft modulation is performed on each iteration of TEQ/SIC/PIC, there is a clear need for a reduced complexity algorithm for converting bit probabilities to soft QAM symbols.